Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
They form a closed set under addition, subtraction or multiplication.
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
Yes they are closed under multiplication, addition, and subtraction.
Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
Arithmetic is the process of applying the four basic operations: addition, subtraction, multiplication and division to numbers.
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
They form a closed set under addition, subtraction or multiplication.
The set of rational numbers is closed under all 4 basic operations.
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
Yes they are closed under multiplication, addition, and subtraction.
There is no counterexample because the set of whole numbers is closed under addition (and subtraction).
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
They are closed under all except that division by zero is not defined.